eig.cc

Go to the documentation of this file.

/*

Copyright (C) 1996-2012 John W. Eaton

This file is part of Octave.

Octave is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

Octave is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
for more details.

You should have received a copy of the GNU General Public License
along with Octave; see the file COPYING.  If not, see
<http://www.gnu.org/licenses/>.

*/

#ifdef HAVE_CONFIG_H
#include <config.h>
#endif

#include "EIG.h"
#include "fEIG.h"

#include "defun-dld.h"
#include "error.h"
#include "gripes.h"
#include "oct-obj.h"
#include "utils.h"

DEFUN_DLD (eig, args, nargout,
  "-*- texinfo -*-\n\
@deftypefn  {Loadable Function} {@var{lambda} =} eig (@var{A})\n\
@deftypefnx {Loadable Function} {@var{lambda} =} eig (@var{A}, @var{B})\n\
@deftypefnx {Loadable Function} {[@var{V}, @var{lambda}] =} eig (@var{A})\n\
@deftypefnx {Loadable Function} {[@var{V}, @var{lambda}] =} eig (@var{A}, @var{B})\n\
Compute the eigenvalues and eigenvectors of a matrix.\n\
\n\
Eigenvalues are computed in a several step process which begins with a\n\
Hessenberg decomposition, followed by a Schur@tie{}decomposition, from which\n\
the eigenvalues are apparent.  The eigenvectors, when desired, are computed\n\
by further manipulations of the Schur@tie{}decomposition.\n\
\n\
The eigenvalues returned by @code{eig} are not ordered.\n\
@seealso{eigs, svd}\n\
@end deftypefn")
{
  octave_value_list retval;

  int nargin = args.length ();

  if (nargin > 2 || nargin == 0 || nargout > 2)
    {
      print_usage ();
      return retval;
    }

  octave_value arg_a, arg_b;

  octave_idx_type nr_a = 0, nr_b = 0;
  octave_idx_type nc_a = 0, nc_b = 0;

  arg_a = args(0);
  nr_a = arg_a.rows ();
  nc_a = arg_a.columns ();

  int arg_is_empty = empty_arg ("eig", nr_a, nc_a);
  if (arg_is_empty < 0)
    return retval;
  else if (arg_is_empty > 0)
    return octave_value_list (2, Matrix ());

  if (!(arg_a.is_single_type () || arg_a.is_double_type ()))
    {
      gripe_wrong_type_arg ("eig", arg_a);
      return retval;
    }

  if (nargin == 2)
    {
      arg_b = args(1);
      nr_b = arg_b.rows ();
      nc_b = arg_b.columns ();

      arg_is_empty = empty_arg ("eig", nr_b, nc_b);
      if (arg_is_empty < 0)
        return retval;
      else if (arg_is_empty > 0)
        return octave_value_list (2, Matrix ());

      if (!(arg_b.is_single_type() || arg_b.is_double_type ()))
        {
          gripe_wrong_type_arg ("eig", arg_b);
          return retval;
        }
    }

  if (nr_a != nc_a)
    {
      gripe_square_matrix_required ("eig");
      return retval;
    }

  if (nargin == 2 && nr_b != nc_b)
    {
      gripe_square_matrix_required ("eig");
      return retval;
    }

  Matrix tmp_a, tmp_b;
  ComplexMatrix ctmp_a, ctmp_b;
  FloatMatrix ftmp_a, ftmp_b;
  FloatComplexMatrix fctmp_a, fctmp_b;

  if (arg_a.is_single_type ())
    {
      FloatEIG result;

      if (nargin == 1)
        {
          if (arg_a.is_real_type ())
            {
              ftmp_a = arg_a.float_matrix_value ();

              if (error_state)
                return retval;
              else
                result = FloatEIG (ftmp_a, nargout > 1);
            }
          else
            {
              fctmp_a = arg_a.float_complex_matrix_value ();

              if (error_state)
                return retval;
              else
                result = FloatEIG (fctmp_a, nargout > 1);
            }
        }
      else if (nargin == 2)
        {
          if (arg_a.is_real_type () && arg_b.is_real_type ())
            {
              ftmp_a = arg_a.float_matrix_value ();
              ftmp_b = arg_b.float_matrix_value ();

              if (error_state)
                return retval;
              else
                result = FloatEIG (ftmp_a, ftmp_b, nargout > 1);
            }
          else
            {
              fctmp_a = arg_a.float_complex_matrix_value ();
              fctmp_b = arg_b.float_complex_matrix_value ();

              if (error_state)
                return retval;
              else
                result = FloatEIG (fctmp_a, fctmp_b, nargout > 1);
            }
        }

      if (! error_state)
        {
          if (nargout == 0 || nargout == 1)
            {
              retval(0) = result.eigenvalues ();
            }
          else
            {
              // Blame it on Matlab.

              FloatComplexDiagMatrix d (result.eigenvalues ());

              retval(1) = d;
              retval(0) = result.eigenvectors ();
            }
        }
    }
  else
    {
      EIG result;

      if (nargin == 1)
        {
          if (arg_a.is_real_type ())
            {
              tmp_a = arg_a.matrix_value ();

              if (error_state)
                return retval;
              else
                result = EIG (tmp_a, nargout > 1);
            }
          else
            {
              ctmp_a = arg_a.complex_matrix_value ();

              if (error_state)
                return retval;
              else
                result = EIG (ctmp_a, nargout > 1);
            }
        }
      else if (nargin == 2)
        {
          if (arg_a.is_real_type () && arg_b.is_real_type ())
            {
              tmp_a = arg_a.matrix_value ();
              tmp_b = arg_b.matrix_value ();

              if (error_state)
                return retval;
              else
                result = EIG (tmp_a, tmp_b, nargout > 1);
            }
          else
            {
              ctmp_a = arg_a.complex_matrix_value ();
              ctmp_b = arg_b.complex_matrix_value ();

              if (error_state)
                return retval;
              else
                result = EIG (ctmp_a, ctmp_b, nargout > 1);
            }
        }

      if (! error_state)
        {
          if (nargout == 0 || nargout == 1)
            {
              retval(0) = result.eigenvalues ();
            }
          else
            {
              // Blame it on Matlab.

              ComplexDiagMatrix d (result.eigenvalues ());

              retval(1) = d;
              retval(0) = result.eigenvectors ();
            }
        }
    }

  return retval;
}

/*

%!assert(eig ([1, 2; 2, 1]), [-1; 3], sqrt (eps));

%!test
%! [v, d] = eig ([1, 2; 2, 1]);
%! x = 1 / sqrt (2);
%! assert(d, [-1, 0; 0, 3], sqrt (eps));
%! assert(v, [-x, x; x, x], sqrt (eps));

%!assert(eig (single ([1, 2; 2, 1])), single([-1; 3]), sqrt (eps('single')));

%!test
%! [v, d] = eig (single([1, 2; 2, 1]));
%! x = single(1 / sqrt (2));
%! assert(d, single([-1, 0; 0, 3]), sqrt (eps('single')));
%! assert(v, [-x, x; x, x], sqrt (eps('single')));

%!test
%! A = [1, 2; -1, 1]; B = [3, 3; 1, 2];
%! [v, d] = eig (A, B);
%! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
%! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));

%!test
%! A = single([1, 2; -1, 1]); B = single([3, 3; 1, 2]);
%! [v, d] = eig (A, B);
%! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single')));
%! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single')));

%!test
%! A = [1, 2; 2, 1]; B = [3, -2; -2, 3];
%! [v, d] = eig (A, B);
%! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
%! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));

%!test
%! A = single([1, 2; 2, 1]); B = single([3, -2; -2, 3]);
%! [v, d] = eig (A, B);
%! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single')));
%! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single')));

%!test
%! A = [1+3i, 2+i; 2-i, 1+3i]; B = [5+9i, 2+i; 2-i, 5+9i];
%! [v, d] = eig (A, B);
%! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
%! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));

%!test
%! A = single([1+3i, 2+i; 2-i, 1+3i]); B = single([5+9i, 2+i; 2-i, 5+9i]);
%! [v, d] = eig (A, B);
%! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single')));
%! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single')));

%!test
%! A = [1+3i, 2+3i; 3-8i, 8+3i]; B = [8+i, 3+i; 4-9i, 3+i];
%! [v, d] = eig (A, B);
%! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
%! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));

%!test
%! A = single([1+3i, 2+3i; 3-8i, 8+3i]); B = single([8+i, 3+i; 4-9i, 3+i]);
%! [v, d] = eig (A, B);
%! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps('single')));
%! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps('single')));

%!test
%! A = [1, 2; 3, 8]; B = [8, 3; 4, 3];
%! [v, d] = eig (A, B);
%! assert(A * v(:, 1), d(1, 1) * B * v(:, 1), sqrt (eps));
%! assert(A * v(:, 2), d(2, 2) * B * v(:, 2), sqrt (eps));

%!error <Invalid call to eig> eig ();
%!error <Invalid call to eig> eig ([1, 2; 3, 4], [4, 3; 2, 1], 1);
%!error eig ([1, 2; 3, 4], 2);
%!error eig ([1, 2; 3, 4; 5, 6]);
%!error eig ("abcd");
%!error eig ([1 2 ; 2 3], "abcd");
%!error eig (false, [1 2 ; 2 3]);

*/